MATH2038 Partial Differential Equations

Module Overview

Differential equations occupy a central role in mathematics because they allow us to describe a wide variety of real-world systems. The module will aim to stress the importance of both theory and applications of differential equations.
The module begins by revisiting some of the material from the first year module on differential equations focussing attention on boundary value problems and also on equations with a source term. We then look at how one can express a general periodic function in terms of Fourier series of sine and cosine functions.
The second section of the module introduces some of the basic concepts of partial differential equations (PDEs). It is shown how PDEs may be used to model situations in a wide variety of situations including biology, finance and applied mathematics. The three important classes of second order PDE appropriate for modelling different sorts of phenomena are introduced and the appropriate boundary conditions for each of these are considered. The technique of separation of variables will be used to reduce the problem to that of solving the sort of ordinary differential equations seen at the start of the module and writing the general solution using Fourier series. Throughout the module there will be a strong emphasis on problem solving and examples.

Module Details

Semester:

Semester 2

CATS points:

15

ECTS points:

7.5

Level:

Level 5

Module Lead:

James Vickers

Aims and Objectives

Module Aims

To stress the importance of both theory and applications of differential equations.

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

Solve simple second order differential equations

Be able to calculate Fourier series

Understand the wide applications of differential equation

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

Prove the Orthogonality of eigenfunctions of boundary value problems

Be able to classify second order partial differential equations and choose the appropriate
boundary conditions

Assessment

Summative

Referral

Repeat Information

Repeat type: Internal & External

Linked modules

Prerequisites: ((MATH1056 OR (MATH1059 AND MATH1060)) AND MATH2039) OR (MATH1006 AND MATH1007)

Costs

Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

Books and Stationery equipment

Course texts are provided by the library and there are no additional compulsory costs associated with
the module.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.